Advances on the Exact Expectation Analyses of Adaptive Filtering Algorithms

Abstract

Adaptive filtering algorithms are flexible and low-cost solutions for many applications where prior knowledge about the statistics of the involved signals is absent. Their sophisticated learning dynamics challenge the design of accurate stochastic models. Most of these models, in the literature adopt the independence theory, which engenders discrepancies between theoretical predictions and actual results. This thesis avoids such a ubiquitous assumption, utilizing the so-called exact expectation analysis, a computationally intensive method that generates more accurate predictions. For the first time, this analysis is employed to model both the case of nonlinear plants and the tracking configuration. Further, it also provides a deterministic sequence of step sizes that optimize the mean-square performance of the LMS under time-variant settings